The complete sublattice of the lattice of convex l -subgroups of an l -group that is generated by its polar subgroups

1997 ◽  
Vol 37 (3) ◽  
pp. 374-390 ◽  
Author(s):  
Z. Xiqiang ◽  
Q. Zhinan
Keyword(s):  
Complete Sublattice

scholarly journals On the lattice of congruences on an eventually regular semigroup

1985 ◽  
Vol 38 (2) ◽  
pp. 281-286 ◽  
Author(s):  
P. M. Edwards
Keyword(s):  
Regular Semigroup ◽  
Subject Classification ◽  
Maximum Element ◽  
M 10 ◽  
Natural Equivalence ◽  
20 M 10 ◽  
Complete Sublattice ◽  
Eventually Regular Semigroup ◽  
Lattice Of Congruences

AbstractA natural equivalence θ on the lattice of congruences λ(S) of a semigroup S is studied. For any eventually regular semigroup S, it is shown that θ is a congruence, each θ-class is a complete sublattice of λ(S) and the maximum element in each θ-class is determined. 1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.

PERMUTATION IDENTITIES AND VARIETIES OF NILSEMIGROUPS

1993 ◽  
Vol 03 (02) ◽  
pp. 201-210
Author(s):  
XIAOYING YAN
Keyword(s):  
Equivalence Relation ◽  
Complete Lattice ◽  
Semigroup Variety ◽  
Infinite Subset ◽  
Equivalence Classes ◽  
Minimal Variety ◽  
Complete Sublattice ◽  
Countably Infinite ◽  
Semigroup Varieties

For any variety V of semigroups there exists a smallest semigroup variety PV containing V and closed for the construction of power semigroups. These varieties PV form a countably infinite subset PL(S) of the lattice L(S) of semigroup varieties. Though (PL(S), ⊆) is a complete lattice, it is not a complete sublattice of L(S). There exists however an interval in L(S) consisting of varieties of nilsemigroups which is isomorphic to (PL(S), ⊆). It will be shown that the equivalence classes of the equivalence relation induced by P: L(S)→PL(S), V↦PV, each contain a unique minimal variety consisting of nilsemigroups.

Congruences on glrac semigroups (I)

2021 ◽  
pp. 2250240
Author(s):  
Haijun Liu ◽  
Xiaojiang Guo
Keyword(s):  
Complete Lattice ◽  
Lattice Homomorphism ◽  
Complete Sublattice ◽  
Restriction Semigroup ◽  
Lattice Of Congruences

The theory of congruences on semigroups is an important part in the theory of semigroups. The aim of this paper is to study [Formula: see text]-congruences on a glrac semigroup. It is proved that the [Formula: see text]-congruences on a glrac semigroup become a complete sublattice of its lattice of congruences. Especially, the structures of left restriction semigroup [Formula: see text]-congruences and the projection-separating [Formula: see text]-congruences on a glrac semigroup are established. Also, we demonstrate that they are both complete sublattice of [Formula: see text]-congruences and consider their relations with respect to complete lattice homomorphism.

scholarly journals Tense Operators on BL-algebras and its Applications

2021 ◽  
Author(s):  
Akbar Paad
Keyword(s):  
Boolean Algebras ◽  
Tense Operators ◽  
Congruence Relations ◽  
Complete Sublattice ◽  
One To One ◽  
Mv Algebras

In this paper, the notions of tense operators and tense filters in \(BL\)-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense \(BL\)-algebras, tense \(MV\)-algebras and tense Boolean algebras are investigated. Moreover, it is shown that the set of all tense filters of a \(BL\)-algebra is complete sublattice of \(F(L)\) of all filters of \(BL\)-algebra \(L\). Also, maximal tense filters and simple tense \(BL\)-algebras and the relation between them are studied. Finally, the notions of tense congruence relations in tense \(BL\)-algebras and strict tense \(BL\)-algebras are introduced and an one-to-one correspondence between tense filters and tense congruences relations induced by tense filters are provided.

The lattice of full regular subsemigroups of a regular semigroup

1984 ◽  
Vol 98 (3-4) ◽  
pp. 203-214 ◽  
Author(s):  
Katherine G. Johnston ◽  
Peter R. Jones
Keyword(s):  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Subdirect Product ◽  
Complete Sublattice ◽  
Principal Factors ◽  
Special Case ◽  
Inverse Subsemigroups ◽  
Completely Semisimple

SynopsisAlthough the regular subsemigroups of a regular semigroup S do not, in general, form a lattice in any naturalway, it is shown that the full regular subsemigroups form a complete sublattice LF of the lattice of all subsemigroups; moreover this lattice has many of the nice features exhibited in (the special case of) the lattice of full inverse subsemigroups of an inverse semigroup, previously studied by one of the authors. In particular, LF is again a subdirect product of the corresponding lattices for each of the principal factors of S.A description of LF for completely 0-simple semigroups is given. From this, lattice-theoretic properties of LF may be found for completely semisimple semigroups. For instance, for any such combinatorial semigroup, LF is semimodular.

On lattices of continuous functions on a Stonian space

2002 ◽  
Vol 132 (1) ◽  
pp. 169-180 ◽  
Author(s):  
D. A. EDWARDS
Keyword(s):  
Continuous Function ◽  
Open Subset ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Extension Theorem ◽  
Continuous Functions ◽  
Complete Sublattice

Suppose that Ω is a compact Hausdorff space with a preorder [les ] whose graph is closed, and let Ω∘ be an open subset of Ω. This paper provides conditions sufficient to allow every increasing bounded real continuous function on Ω∘ to be extended to an increasing real continuous function on Ω. These conditions are: (i) that Ω is a Stonian space, and (ii) that the set C↑(Ω, [les ]) of increasing real continuous functions on Ω is a regular Dedekind complete sublattice of C(Ω). Under these conditions it is also shown that C↑(Ω, [les ]) is generated by idempotents, and an extension theorem for idempotents is proved.

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